%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU327+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:45:49 AM UTC 2026
% Result : Theorem 0.22s 0.84s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 21 unt; 0 def)
% Number of atoms : 72 ( 39 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 24 ~; 14 |; 5 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 46 ( 1 sgn 20 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_subset_1,axiom,
! [A] : cast_to_subset(A) = A,
file('theBenchmark.p',d4_subset_1) ).
fof(d5_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('theBenchmark.p',d5_subset_1) ).
fof(dt_k5_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(union_of_subsets(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k5_setfam_1) ).
fof(redefinition_k5_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> union_of_subsets(A,B) = union(B) ),
file('theBenchmark.p',redefinition_k5_setfam_1) ).
fof(redefinition_k6_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_difference(A,B,C) = set_difference(B,C) ),
file('theBenchmark.p',redefinition_k6_subset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t47_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> subset_difference(A,cast_to_subset(A),union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B)) ) ),
file('theBenchmark.p',t47_setfam_1) ).
fof(t11_tops_2,conjecture,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> meet_of_subsets(A,complements_of_subsets(A,B)) = subset_complement(A,union_of_subsets(A,B)) ) ),
file('theBenchmark.p',t11_tops_2) ).
fof(t11_tops_2_neg,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> meet_of_subsets(A,complements_of_subsets(A,B)) = subset_complement(A,union_of_subsets(A,B)) ) ),
inference(assume_negation,[status(cth)],[t11_tops_2]) ).
cnf(c_61,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
cnf(c_62,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_63,plain,
element(A,powerset(A)),
inference(resolve,[status(thm)],[c_62,c_61]) ).
cnf(c_89,plain,
cast_to_subset(A) = A,
inference(clausify,[status(thm)],[d4_subset_1]) ).
cnf(c_90,plain,
( set_difference(B,A) = subset_complement(B,A)
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[d5_subset_1]) ).
cnf(c_91,plain,
( subset_complement(B,A) = set_difference(B,A)
| ~ element(A,powerset(B)) ),
inference(copy,[status(thm)],[c_90]) ).
cnf(c_94,plain,
( element(union_of_subsets(B,A),powerset(B))
| ~ element(A,powerset(powerset(B))) ),
inference(clausify,[status(thm)],[dt_k5_setfam_1]) ).
cnf(c_133,plain,
( union(A) = union_of_subsets(B,A)
| ~ element(A,powerset(powerset(B))) ),
inference(clausify,[status(thm)],[redefinition_k5_setfam_1]) ).
cnf(c_134,plain,
( union_of_subsets(B,A) = union(A)
| ~ element(A,powerset(powerset(B))) ),
inference(copy,[status(thm)],[c_133]) ).
cnf(c_137,plain,
( subset_difference(B,A,C) = set_difference(A,C)
| ~ element(C,powerset(B))
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[redefinition_k6_subset_1]) ).
cnf(c_141,plain,
( subset_difference(B,cast_to_subset(B),union_of_subsets(B,A)) = meet_of_subsets(B,complements_of_subsets(B,A))
| empty_set = A
| ~ element(A,powerset(powerset(B))) ),
inference(clausify,[status(thm)],[t47_setfam_1]) ).
cnf(c_142,plain,
( subset_difference(B,B,union_of_subsets(B,A)) = meet_of_subsets(B,complements_of_subsets(B,A))
| empty_set = A
| ~ element(A,powerset(powerset(B))) ),
inference(paramod,[status(thm)],[c_89,c_141]) ).
fof(nnf_59,plain,
? [A,B] :
( meet_of_subsets(A,complements_of_subsets(A,B)) != subset_complement(A,union_of_subsets(A,B))
& empty_set != B
& element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[t11_tops_2_neg]) ).
fof(sk_t11_tops_2_neg,plain,
( meet_of_subsets(sK1,complements_of_subsets(sK1,sK0)) != subset_complement(sK1,union_of_subsets(sK1,sK0))
& empty_set != sK0
& element(sK0,powerset(powerset(sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_59]) ).
cnf(c_149,negated_conjecture,
element(sK0,powerset(powerset(sK1))),
inference(split_conjunct,[status(thm)],[sk_t11_tops_2_neg]) ).
cnf(c_150,negated_conjecture,
empty_set != sK0,
inference(split_conjunct,[status(thm)],[sk_t11_tops_2_neg]) ).
cnf(c_151,negated_conjecture,
meet_of_subsets(sK1,complements_of_subsets(sK1,sK0)) != subset_complement(sK1,union_of_subsets(sK1,sK0)),
inference(split_conjunct,[status(thm)],[sk_t11_tops_2_neg]) ).
cnf(c_152,negated_conjecture,
subset_complement(sK1,union_of_subsets(sK1,sK0)) != meet_of_subsets(sK1,complements_of_subsets(sK1,sK0)),
inference(copy,[status(thm)],[c_151]) ).
cnf(c_287,plain,
( subset_difference(B,B,A) = set_difference(B,A)
| ~ element(A,powerset(B)) ),
inference(resolve,[status(thm)],[c_137,c_63]) ).
cnf(c_1825,negated_conjecture,
( subset_difference(sK1,sK1,union_of_subsets(sK1,sK0)) = meet_of_subsets(sK1,complements_of_subsets(sK1,sK0))
| empty_set = sK0 ),
inference(resolve,[status(thm)],[c_149,c_142]) ).
cnf(c_331,negated_conjecture,
subset_difference(sK1,sK1,union_of_subsets(sK1,sK0)) = meet_of_subsets(sK1,complements_of_subsets(sK1,sK0)),
inference(resolve,[status(thm)],[c_150,c_1825]) ).
cnf(c_336,plain,
union_of_subsets(sK1,sK0) = union(sK0),
inference(resolve,[status(thm)],[c_149,c_134]) ).
cnf(c_1826,negated_conjecture,
element(union_of_subsets(sK1,sK0),powerset(sK1)),
inference(resolve,[status(thm)],[c_149,c_94]) ).
cnf(c_343,negated_conjecture,
element(union(sK0),powerset(sK1)),
inference(paramod,[status(thm)],[c_336,c_1826]) ).
cnf(c_361,negated_conjecture,
subset_difference(sK1,sK1,union(sK0)) = meet_of_subsets(sK1,complements_of_subsets(sK1,sK0)),
inference(paramod,[status(thm)],[c_336,c_331]) ).
cnf(c_362,negated_conjecture,
subset_complement(sK1,union(sK0)) != meet_of_subsets(sK1,complements_of_subsets(sK1,sK0)),
inference(paramod,[status(thm)],[c_336,c_152]) ).
cnf(c_641,plain,
subset_complement(sK1,union(sK0)) = set_difference(sK1,union(sK0)),
inference(resolve,[status(thm)],[c_343,c_91]) ).
cnf(c_659,negated_conjecture,
set_difference(sK1,union(sK0)) != meet_of_subsets(sK1,complements_of_subsets(sK1,sK0)),
inference(paramod,[status(thm)],[c_641,c_362]) ).
cnf(c_1827,plain,
subset_difference(sK1,sK1,union(sK0)) = set_difference(sK1,union(sK0)),
inference(resolve,[status(thm)],[c_287,c_343]) ).
cnf(c_1828,plain,
meet_of_subsets(sK1,complements_of_subsets(sK1,sK0)) = set_difference(sK1,union(sK0)),
inference(paramod,[status(thm)],[c_361,c_1827]) ).
cnf(c_1829,plain,
set_difference(sK1,union(sK0)) = meet_of_subsets(sK1,complements_of_subsets(sK1,sK0)),
inference(copy,[status(thm)],[c_1828]) ).
cnf(c_1824,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_659,c_1829]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU327+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.64 % Computer : n009.cluster.edu
% 0.18/0.64 % Model : x86_64 x86_64
% 0.18/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.64 % Memory : 8046.5625MB
% 0.18/0.64 % OS : Linux 6.8.0-71-generic
% 0.18/0.64 % CPULimit : 300
% 0.18/0.64 % WCLimit : 300
% 0.18/0.64 % DateTime : Sat Sep 26 09:13:01 UTC 2026
% 0.18/0.64 % CPUTime :
% 0.18/0.65 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.65 % Process 3946296 was started by sandbox2 on n009,
% 0.18/0.65 % Sat Sep 26 09:13:01 2026
% 0.18/0.65 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.22/0.67
% 0.22/0.67 % From the command line: assign(max_seconds, 300).
% 0.22/0.84
% 0.22/0.84 % SZS status Theorem for theBenchmark
% 0.22/0.84
% 0.22/0.84 % Proof 1 at 0.11 (+ 0.05) seconds.
% 0.22/0.84 % Length of proof is 34.
% 0.22/0.84 % Level of proof is 7.
% 0.22/0.84 % Maximum clause weight is 40.000.
% 0.22/0.84 % Given clauses 387.
% 0.22/0.84
% 0.22/0.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------